Question

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

• A. 40 ms$^{-1}$
• B. 120 ms$^{-1}$
• C. 100 ms$^{-1}$
• D. 80 ms$^{-1}$

Answer 1

The Correct Option is C

mv = Mv' $\Rightarrow \, \, \, \, v' =\bigg(\frac{m}{M}\bigg)v$
Total K.E. of the bullet and gun
$=\frac{1}{2}mv^2+\frac{1}{2}Mv'{^2}$
Total K.E =$\frac{1}{2}mv^2+\frac{1}{2}M\cdot \frac{m^2}{M^2}v^2$
Total K.E =$\frac{1}{2}mv^2 \bigg \{1+\frac{m}{M}\bigg \}$
$ \, \, \, \, \, = \bigg \{ \frac{1}{2} \times \, 0.2 \bigg \} \bigg\{ 1+\frac{0.2}{4}\bigg\} v^2=1.05 \times 1000\, J$
$\Rightarrow \, \, \, \, v^2=\frac{4 \times \, 1.05 \, \times 1000}{0.1 \, \times \, 4.2}=100^2$;
$\therefore \, \, \, v=100 \,ms^{-1}$